In maths, the average is the middle value of a set of numbers. This isn’t to be confused with the median, the middle of a group of numbers. The average is the median value of the numbers. If you need to find the standard of a set of numbers, you add them all together and divide by the number of digits. You can do this with any group of numbers, no matter how far apart the values of the numbers are. That’s the beauty of finding the average!

The average is a valuable piece of information. It’s mainly used in maths and statistics to overview a large amount of data quickly. When you have the standard, you have an estimate of the process that’s been undertaken. For example, if you find the average results of people taking tests, you can determine an estimation of how the results would turn out if the test is done again. This is useful in statistics because it means you can analyze large amounts of results without repeatedly redoing them. So, the next time someone asks, “what is the average?” you can tell them!

**How To Work Out An Average**

There are three main average types: mean, median, and mode.

We use mean, median, and mode averages to give information about a data set. These are different types of standards, so other methods are used to work out each.

To work out an average, you must add all the numbers in the set. Then, you divide the total sum by the number of digits. For example, for the set of numbers 3, 4, and 8, you add them together and get 15. Then, you divide by three and get 5. 5 is the average.

**Here is how you work out different types of averages:**

- The mean is the average number in a set of numbers, which gives us an idea about the overall trends within the data. It is calculated by adding all the numbers and dividing by the total.
- The median is worked out by listing the numbers in order of size and finding the middle one.
- The mode is the most commonly occurring number within the data.

**Average Formula**

Any time you are presented with a data set and asked to find the average, you can use a quick and easy formula. The average formula is as follows:

Average = Total Sum of All Numbers ÷ Number of Items in the Set

**Examples of Finding the Average**

Let’s put your knowledge of finding the average to the test with some examples.

Example 1: Jenny celebrated her 15th birthday last week with a trip to her favorite beach. Jenny invited six of her closest friends to go with her: Danielle, who is 15, Caroline, who is 17, Katy, who is 15, Rebecca, who is 16; Janet, who is 20; and Emma, who is 19. Also, on the beach trip, Jenny’s mum, Elizabeth, is 55 years old. What was the average age of the people on Jenny’s birthday beach trip?

Average formula:

Average = Total Sum of All Numbers ÷ Number of Items in the Set

The first step in finding the average is to add up the ages of everyone on Jenny’s beach trip. So

15 + 15 + 17 + 15 + 16 + 20 + 19 + 55

= 172

Now, let’s put this number into our formula:

Average = 172 ÷ Number of Items in the Set

There were six friends at Jenny’s birthday so, including her mum, eight people were there. Let’s put that number into our formula:

Average = 172 ÷ 8

Now, all we have to do is divide 172 by 8, and we will have found the average age of the people on Jenny’s birthday beach trip!

Average = 21.5

So, the average age of people there was 21.5 years old.

Example 2: Last week, Class B took an important maths test, and the teacher was finally ready to give them back their marks. There were 30 people in Class B. The test was marked out of 100. The test scores for Class B were as follows: 10 students got 80, 5 students got 95, 3 students got 62, 2 students got 77, 6 students got 50, 3 students got 91, and 1 student got 100. What was the average test score for Class B?

Average formula:

Average = Total Sum of All Numbers ÷ Number of Items in the Set

The first step in finding the average is adding all the scores together. So

(80 × 10) + (95 × 5) + (62 × 3) + (77 × 2) + (50 × 6) +(91 × 3) + 100

This step is a bit more complicated than the one in the previous example, as multiplication is involved. However, the easiest way to approach this sum is to solve the brackets before adding.

80 × 10 = 800

95 × 5 = 475

62 × 3 = 186

77 × 2 = 154

50 × 6 = 300

91 × 3 = 273

100 × 1 = 100

All of our brackets have been solved, so we can just put these numbers into our sum and carry out the addition.

800 + 475 + 186 + 154 + 300 + 273 + 100

= 2,288

Now, let’s put that number into our average formula:

Average = 2,288 ÷ Number of Items in the Set

There are 30 students in Class B, which means that

Average = 2,288 ÷ 30

Now, all we have to do to find the average test score for Class B is divide 2,288 by 30. However, this is a significant sum, so you may need a calculator!

Average = 76.2

So, the average test score for Class B was 76.2 out of 100

Example 3: Rachel wants to buy a new skirt, so she has been saving her pocket money for six weeks. She gets £5 a week from her parents, so she has managed to keep a total of £30. She has been looking online and has narrowed it down to her five favorite skirts. The most expensive skirt costs only £30, while the cheapest is only £12. The prices of the other dresses are £25, £17, and £28. Work out the average cost of Rachel’s five favorite skirts.

Average formula:

Average = Total Sum of All Numbers ÷ Number of Items in the Set

The first step in finding the average is adding all the skirts’ prices. So

30 + 12 + 25 + 17 + 28

= 112

Now, let’s put that number into our formula:

Average = 112 ÷ Number of Items in the Set

There are five skirts that Rachel is choosing between, which means that

Average = 112 ÷ 5

Now, to find the average price of the skirts, we have to divide 112 by 5.

Average = 22.4

So, the average price of the skirts is £22.40